In this paper, we looked at the so-called relative velocity effect in the large-scale structure of the Universe. To understand this effect we need to go through three areas of cosmology:
(1) The building blocks and evolution of the Universe
(2) Baryon Acoustic Oscillations (BAO)
(3) The basics of galaxy redshift surveys
I will go through all three of these points in turn and bring them together in the end. But before I start here is a general overview to see how these three points fit together.
If you want to test a theory, what you have to do is you have to look at what this theory predicts and see whether you can confirm or disprove this prediction with data. Such tests are fundamental to the progress of science. For many cosmological theories the most powerful tests we currently have involve Baryon Acoustic Oscillations (BAO) in the photon and matter distribution. Below I will discuss exactly what BAO are but for now, just see it as a test to distinguish cosmological models.
In the paper I want to discuss here, we looked at the relative velocity effect. As the name suggests, it describes a relative velocity, in this case, a relative velocity between cold dark matter and baryonic matter. This relative velocity can impact galaxy formation, meaning the types of galaxies which form and the places where they form. These changes can impact our measurement of Baryon Acoustic Oscillations from galaxy redshift surveys. Given the importance of BAO for cosmological studies, we need to understand the impact of this relative velocity otherwise we might draw the wrong conclusion from such measurements.
In the rest of this blog post, I will describe the origin of the relative velocity, its impact on galaxy formation and how this could influence what we measure with galaxy redshift surveys.
The building blocks and evolution of the Universe
The Universe is made up of baryonic matter (protons, electrons etc), cold dark matter (we don't know what particle cold dark matter is made of) and dark energy (we don't know much about that either). Dark Energy is a force which causes the Universe to expand at late times, but it is not relevant for this paper, so let's focus on baryonic matter and cold dark matter.
The main difference between baryons and cold dark matter is the fact that cold dark matter does not have an electric charge. This is crucial since if it had an electric charge, it would interact with photons and interaction with photons would mean that we can see it. The reason why cold dark matter is called dark is because we cannot directly see it (no photons scatter on it). The only reason we know it is there is because we can see the gravitational effects it has (for example through gravitational lensing experiments).
Ok, let us go through the different stages of the Universe's evolution and see how they impact the two main components we are interested in (baryons and cold dark matter).
(1) The beginning, inflation:
The Universe starts off with a period of very quick expansion, which is driven by the so called inflaton field and only lasts for a tiny fraction of a second. The theory of inflation is observationally not very well tested and fairly speculative at this point. But it provides the right initial conditions for the next steps of the Universe's evolution.
For this discussion, the most important aspect of inflation is that it introduced tiny density fluctuations into the matter density field, which are going to be the places where galaxies will form later on.
(2) Plasma phase:
After inflation, the Universe is so hot and dense that it does not allow atoms to form. For some time even quarks, which form the nuclei of atoms, are free. Since the Universe expands, it cools over time. After about $300\,000$ years the Universe cooled enough so that atoms could form, mostly neutral hydrogen.
The period before the formation of neutral hydrogen is the crucial period for this discussion because in those $300\,000$ years, dark matter and baryonic matter followed a very different path of evolution. The difference is caused by the electric charge. The baryons interact with each other through the exchange of photons which is possible because of their electric charge. Wherever you have a density of baryons, you have a density of photons and this causes a photon pressure which pushes the baryons out of the overdensity.
Cold dark matter does not interact with photons, because it does not have an electric charge. Therefore, wherever you have a higher density of cold dark matter, gravity is pulling the matter together, causing the density to increase. So while photon pressure prevents the baryon density to grow at any point in the Universe, gravity causes the cold dark matter density to grow.
(3) The dark ages:
After $300\;000$ years the Universe cooled enough for protons to capture electrons to form neutral hydrogen. As the name suggests, this form of hydrogen is neutral, since it is made up of one proton and one electron, and the electric charges they carry cancel out. This means that now baryonic matter stops interacting with photons because in the form of neutral hydrogen, baryons do not have an electric charge anymore.
Without the photon interaction, there is no photon pressure and without photon pressure, the baryon density can grow just like the cold dark matter density did all along. The reason this period of the Universe's evolution is called the dark age is because none of the matter interacts with photons. Since photons are what we can see with telescopes, we can't see anything in that era.
(4) Reionisation:
During the dark ages the density of baryons and dark matter grows and at some point, the temperature in the high-density regions grows enough so that the hydrogen ionizes again (protons and electrons separate). In principle we would now expect to go back to the physics we described during the plasma phase, however, the photon density is much lower now. Therefore the photon pressure isn't a big deal anymore and the evolution of baryons is determined by other processes. These processes lead to the formation of stars and galaxies.
Cold dark matter does not interact and hence it can't form stars. Therefore cold dark matter concentrates in so-called haloes and galaxies form in the center of these haloes.
The important phase for the subject discussed in our paper is phase (2) the plasma phase. During this time the baryon density cannot grow, while the cold dark matter density does grow. This means that baryons and cold dark matter start off in phase (3) with a different density distribution.
Besides the difference in the density, there is also a difference in the velocity because the cold dark matter was moving towards high-density regions (driven by gravity), while baryons were moving out of high-density regions (driven by the photon pressure).
So the main point we have to keep in mind is that there is a relative velocity between cold dark matter and baryons due to the physical processes which happened in the plasma phase of the Universe.
Next, we need to discuss Baryon Acoustic Oscillations.
Baryon Acoustic Oscillations
Baryon Acoustic Oscillations are a signal in the matter distribution which can be used to test cosmological models. So what are Baryon Acoustic Oscillations?
As I mentioned before, in the plasma phase the baryon density cannot grow. Instead, wherever there is an over-density, the photon pressure drives all baryons out in a spherical wave. This wave never stops but travels for the entire $300\,000$ years until the photons and the baryons decouple. Only at this point does the wave stops.
This, however, leads to a strange distribution of matter. The initial over-density, which the baryons got kicked out of because of photon pressure, grew due to the infall of cold dark matter. So now we have an overdensity in the center and a shell of baryons around it. The radius of this shell depends on the speed the wave traveled.
These processes happened at every over-density in the Universe and hence at the end of the plasma phase, the Universe is a superposition of such structures. The main point here is that these over-densities (the overdensity in the center, which grew through the infall of cold dark matter and the baryonic shell) are the seeds where galaxies will form later on.
However, this introduces a special scale in the distribution of galaxies, namely the radius of the shell. So if you look at the separation between galaxies, you will find an excess of galaxies separated by the radius of this shell. This special scale is what we call Baryon Acoustic Oscillations, and this scale is one of the most important observational tools we have in Cosmology.
Next, we need to discuss the principles of galaxy redshift surveys.
Galaxy redshift surveys
One important tool to study the Universe is galaxy redshift surveys. Such surveys measure the 3D position of galaxies. I am currently working for the BOSS (Baryon Oscillation Spectroscopic Survey) Collaboration which in the last 6 years composed a galaxy redshift survey with about 1 million galaxies, representing the biggest such survey currently available.
With such a survey we can measure Baryon Acoustic Oscillations since we have the position of the galaxies. As I mentioned, BAO are just a special separation scale of galaxies, so we look at all galaxy pairs, count how many we have and search for the scale where we suddenly get more pairs. This is the Baryon Acoustic scale and we can use that to learn about the expansion history of the Universe.
When we construct a galaxy redshift survey we pick a certain kind of galaxy, in BOSS we picked so-called Luminous Red Galaxies (LRGs), and observe them everywhere in the sky. We can only observe baryons (galaxies), since cold dark matter does not send any photons which we could observe with a telescope.
However, if we want to learn something about the Universe we need to know the entire matter distribution, not just the distribution of galaxies. Therefore we use galaxies to trace the underlying matter density field. The idea behind this is that wherever we have more baryons, we will also have more cold dark matter.
The statistical assumptions we make when using LRGs to trace the matter density field are:
(1) We assume that galaxies are related to the underlying matter density field by a bias relation
\[
\text{galaxy density} = b(r)*\text{matter density},
\]where $b(r)$ is the so-called bias parameter, and it allows us to study the matter distribution, even though we only observe galaxies.
(2) We assume that the galaxies we use as tracers have the same relation b(r) to the matter density field everywhere in the Universe, meaning the probability to find a LRG galaxy at any point in the Universe only depends on the matter density field and nothing else.
We will get back to these assumptions very soon because the relative velocity between baryons and cold dark matter potentially violates these assumptions, which is the reason we wrote the paper.
Bringing it all together
The relative velocity between cold dark matter and baryons is expected to be something like 30km/s at the beginning of the plasma phase but decreases over time meaning the baryons catch up with the cold dark matter and their relative velocity today is expected to be only 0.03km/s.
A relative velocity of 0.03km/s today is completely negligible, for example the velocities in galaxy groups are typically $100$ - $1000\,$km/s. However, at the times when the first galaxies form, this relative velocity is around $1$-$3\,$km/s. If the baryons have a relative velocity with respect to cold dark matter, they might be able to escape the gravitational potential of small cold dark matter halos.
This means, within such dark matter halos, there are fewer baryons available for galaxy formation. This might impact what kind of galaxies form in areas of the Universe where the relative velocity is large.
Now you can understand why the relative velocity is potentially interesting for people who study the formation of galaxies. The problem is that we do not understand galaxy formation very well. There are physical processes like supernovae feedback, AGN feedback, gas cooling and many many more, which are very difficult to simulate. But let's ignore the implications for galaxy formation for now. Why is this interesting for galaxy redshift surveys?
As stated above, we assume that the probability to form a LRG galaxy is only dependent on the matter density. The impact of the relative velocity means that the probability to observe a LRG galaxy also depends on the value of the relative velocity at that point in the Universe. So the relative velocity violates assumption (2) made above.
What did we do in the paper?
Even though the relative velocity violates assumption (2) of our galaxy redshift survey analysis above, everything is not lost. We can actually account for this effect, by modifying the relation $b(r)$ given in assumption (1). So we basically account for the fact that the probability to find a LRG galaxy might depend on where we look in the Universe.
The paper we published develops a model for the relative velocity effect, which we fit to the BOSS data. Long story short, we did not detect the relative velocity effect. However, with this test we ensured that the potential impact of the relative velocity effect for our BAO measurements in BOSS is smaller than our current measurement uncertainties. This increases our confidence in the BOSS analysis and in any cosmological implications one might draw from this measurement. I expect that all future galaxy survey studies of BAO need to check this additional effect, to ensure that they are not systematically biased.
Finally I am very interested to learn more about what this effect could mean for galaxy formation itself. If it would be possible to understand what impact the relative velocity effect has on galaxy formation, we might get another signal to look for to measure this effect. And maybe we can even improve our galaxy formation models.
Ok I hope that was helpful. If you have any questions feel free to leave a comment below.
cheers
Florian
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